This report is the result of the use of the python package bgc_md, as means to translate published models to a common language. The underlying yaml file was created by Verónika Ceballos-Núñez (Orcid ID: 0000-0002-0046-1160) on .
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Trugman et al. (2018).
| Name | Description | Unit |
|---|---|---|
| \(C\) | Non-structural carbon (NSC), starch | \(kgC\cdot m^{-2}\) |
| \(X\) | Xylem biomass | \(kgC\cdot m^{-2}\) |
| \(L\) | Leaf and fine roots biomass which are linearly related through a constant | \(kgC\cdot m^{-2}\) |
| Name | Description | Unit |
|---|---|---|
| \(t\) | time step | \(month\) |
| \(A_{n}\) | whole-plant net photosynthesis (classic photosynthetic model of CO2 demand for carbon-limited photosynthesis), function of the interstitial CO2 concentration, the daytime leaf respiration, the maximum rate of carboxylation, and empirical constants | - |
| Name | Description | Expression |
|---|---|---|
| \(C_{i}\) | initial NSC that covers carbon for two crown and fine root flushes | - |
| \(W_{max}\) | Maximum m sucrose loading rate and depends on tree size. | - |
| \(k_{c}\) | Michaelis constant for the sucrose loading rate | - |
| \(W\) | Sucrose loading rate from storage to the phloem | \(W=\frac{C\cdot W_{max}}{C + C_{i}\cdot k_{c}}\) |
| \(L_{opt}\) | Optimal total leaf biomass | - |
| \(U\) | Variable optimized in the system in the range [0,1]. Fraction of translocatable C invested in xylem reconstruction | \(U=\frac{X\cdot\left(- L_{opt}\cdot\left(m_{L} + m_{X}\right) + W\right)}{W\cdot\left(L_{opt} + X\right)}\) |
| Name | Description | Unit |
|---|---|---|
| \(m_{X}\) | Turnover rate of the xylem | \(month^{-1}\) |
| \(m_{L}\) | Turnover rate of the xylem | \(month^{-1}\) |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}C\\X\\L\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=A_{n}\) |
| \(\beta\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(\beta=\left[\begin{matrix}1\\0\\0\end{matrix}\right]\) |
| \(B\) | matrix of cycling rates | \(B=\left[\begin{matrix}-\frac{W}{C} & 0 & 0\\\frac{U\cdot W}{C} & - m_{X} & 0\\\frac{W\cdot\left(1 - U\right)}{C} & 0 & - m_{L}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u\beta + B x\) |
\(C: A_{n}\)
\(X: X\cdot m_{X}\)
\(L: L\cdot m_{L}\)
\(C \rightarrow X: \frac{X\cdot\left(C\cdot W_{max} - L_{opt}\cdot\left(C + C_{i}\cdot k_{c}\right)\cdot\left(m_{L} + m_{X}\right)\right)}{\left(C + C_{i}\cdot k_{c}\right)\cdot\left(L_{opt} + X\right)}\)
\(C \rightarrow L: \frac{C\cdot W_{max}\cdot\left(L_{opt} + X\right) - X\cdot\left(C\cdot W_{max} - L_{opt}\cdot\left(C + C_{i}\cdot k_{c}\right)\cdot\left(m_{L} + m_{X}\right)\right)}{\left(C + C_{i}\cdot k_{c}\right)\cdot\left(L_{opt} + X\right)}\)
\(C = -\frac{A_{n}\cdot C_{i}\cdot k_{c}}{A_{n} - W_{max}}\)
\(X = 0\)
\(L = \frac{A_{n}}{m_{L}}\)
\(C = -\frac{A_{n}\cdot C_{i}\cdot k_{c}}{A_{n} - W_{max}}\)
\(X = \frac{A_{n} - L_{opt}\cdot m_{L} - 2\cdot L_{opt}\cdot m_{X}}{m_{X}}\)
\(L = \frac{L_{opt}\cdot\left(m_{L} + 2\cdot m_{X}\right)}{m_{L}}\)
Trugman, A. T., Detto, M., Bartlett, M. K., Medvigy, D., Anderegg, W. R. L., Schwalm, C., … Pacala, S. W. (2018). Tree carbon allocation explains forest drought-kill and recovery patterns. Ecology Letters, 21(10), 1552–1560. http://doi.org/10.1111/ele.13136